A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka- ojasiewicz condition

arXiv:2608.05460 · math.OC, cs.LG · Submitted 2026-08-05 · Read on arXiv

Felipe Atenas, Alejandro Jofré, Pedro Pérez-Aros, David Torregrosa-Belén

math.OC, cs.LG

Submitted: 2026-08-05

Updated: 2026-08-10

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Quantization — 22× in this paper · explained in 15 episodes
• Regularization — 8× in this paper · explained in 3 episodes
• Convergence Guarantees — 7× in this paper · explained in 3 episodes
• Proximal Stochastic Subgradient — 6× in this paper
• Objective Function — 5× in this paper · explained in 2 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Clustering — 2× in this paper · explained in 2 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Localization — 2× in this paper · explained in 2 episodes
• Sparsity — 2× in this paper · explained in 5 episodes
• Variance Reduction — 2× in this paper · explained in 2 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Leveraging the Kurdyka-Lojasiewicz — 1× in this paper
• Society for Industrial and Applied Mathematics — 1× in this paper
• Surrogate Model — 1× in this paper · explained in 3 episodes

Sources

• Nonmonotone subgradient methods based on a local descent lemma
• Shadow splitting methods for nonconvex optimisation: epi-approximation, convergence and saddle point avoidance
• A Nonmonotone Descent Method for Optimization Problems Defined by Upper-$\mathcal{C}^2 $ Functions over Submanifolds
• Randomized block proximal method with locally Lipschitz continuous gradient

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